II M.Sc(Mathematics) I Internal Marks 2019-20

UG & PG Almanac 2019-20

UG Result Analysis 2018-19

Exam fee Notification for UG

PG Syllabus 2019-20 semester 1 & 2

DEPARTMENT OF MATHEMATICS, OSMANIA UNIVERSITY 

(Choice Based Credit System)

 (w.e.f. the academic year 2018-2019) 

M. Sc. MATHEMATICS 

SEMESTER – I

MM 101                                                                                                                                Semester-I Paper-I: Abstract Algebra 

Unit-I 

Automorphisms - Conjugacy and G - sets - Normal series Solvable groups - Nilpotent groups.

 (Pages 104 to 128 of [1]) 

Unit-II 

    Structure theorems of groups: Direct product - Finitely generated abelian groups - Invariants of a finite abelian group - Sylow’s theorems - Groups of orders p2 , pq . (Pages 138 to 155)

 Unit-III 

     Ideals and homomorphisms - Sum and direct sum of ideals, Maximal and prime ideals - Nilpotent and nil ideals - Zorn’s lemma (Pages 179 to 211).

 Unit-IV

    Unique factorization domains - Principal ideal domains - Euclidean domains - Polynomial rings over UFD - Rings of Fractions.(Pages 212 to 228) 

Text Book: Basic Abstract Algebra by P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul.

 Reference:

 [1] Topics in Algebra by I.N. Herstein.

 [2] Elements of Modern Algebra by Gibert& Gilbert. 

 [3] Abstract Algebra by Jeffrey Bergen. 

[4] Basic Abstract Algebra by Robert B Ash

MM 102                                                                                                                             Semester - I                                                       Paper - II: Mathematical Analysis

 Unit-I

 Metric spaces - Compact sets - Perfect sets - Connected sets.

 Unit-II

 Limits of functions - Continuous functions - Continuity and compactness, Continuity and connectedness - Discontinuities - Monotone functions. 

Unit-III 

Riemann - Steiltjes integral - Definition and Existence of the Integral - Properties of the integral - Integration of vector valued functions - Rectifiable curves.

 Unit-IV

 Sequences and series of functions: Uniform convergence - Uniform convergence and continuity - Uniform convergence and integration - Uniform convergence and differentiation - Approximation of a continuous function by a sequence of polynomials. 

Text Book:

 Principles of Mathematical Analysis (3rd Edition) (Chapters 2, 4, 6 ) By Walter Rudin, Mc Graw - Hill Internation Edition.

 References:

 [1] The Real Numbers by John Stillwel.

 [2] Real Analysis by Barry Simon 

[3] Mathematical Analysis Vol - I by D J H Garling.

 [4] Measure and Integral by Richard L.Wheeden and Antoni Zygmund. 

MM 103                                                                                                                           Semester - I                                    Paper - III: Ordinary and Partial Differential Equations

 Unit-I

 Existence and Uniqueness of solution of dy dx = f(x, y) and problems there on. The method of successive approximations - Picard’s theorem - Non - Linear PDE of order one - Charpit’s method - Cauchy’s method of Characteristics for solving non - linear partial differential equations - Linear Partial Differential Equations with constant coefficients.

 Unit-II 

Partial Differential Equations of order two with variable coefficients - Canonical form - Classification of second order Partial Differential Equations - separation of variables method of solving the one - dimensional Heat equation, Wave equation and Laplace equation - Sturm - Liouville’s boundary value problem.

 Unit-III

 Power Series solution of O.D.E. Ordinary and Singular points - Series solution about an ordinary point - Series solution about Singular point - Frobenius Method. Lagendre Polynomials: Lengendre’s equation and its solution - Lengendre Polynomial and its properties - Generating function - Orthogonal properties - Recurrance relations - Laplace’s definite integrals for Pn(x) - Rodrigue’s formula. 

Unit-IV

 Bessels Functions: Bessel’s equation and its solution - Bessel function of the first kind and its properties - Recurrence Relations - Generating function - Orthogonality properties. Hermite Polynomials: Hermite’s equation and its solution - Hermite polynomial and its properties - Generating function - Alternative expressions (Rodrigue’s formula) - Orthogonality properties - Recurrence Relations.

 Text Books: 

[1] Ordinary and Partial Differential Equations, By M.D. Raisingania, S. Chand Company Ltd., New Delhi. 

[2] Text book of Ordinary Differential Equation, By S.G.Deo, V. Lakshmi Kantham, V. Raghavendra, Tata Mc.Graw Hill Pub. Company Ltd.

 [3] Elements of Partial Differential Equations, By Ian Sneddon, Mc.Graw - Hill International Edition.

 Reference:

 [1] Worldwide Differential equations by Robert McOwen .

 [2] Differential Equations with Linear Algebra by Boelkins, Goldberg, Potter. 

[3] Differential Equations By Paul Dawkins. 

MM 104                                                                                                                        Semester - I                                                Paper - IV: Elementary Number Theory

 Unit-I 

The Fundamental Theorem of arithmetic: Divisibility, GCD, Prime Numbers, Fundamental theorem of Arithemtic, the series of reciprocal of the Primes, The Euclidean Algorithm. 

Unit-II 

Arithmetic function and Dirichlet Multiplication, The functions φ(n), µ(n) and a relation connecting them, Product formulae for φ(n), Dirichlet Product, Dirichlet inverse and Mobius inversion formula and Mangoldt function Λ(n), multiplication function, multiplication function and Dirichlet multiplication, Inverse of a completely multiplication function, Liouville’s function λ(n), the divisor function is σα(n) 

Unit-III

 Congruences, Properties of congruences, Residue Classes and complete residue system, linear congruences conversion, reduced residue system and Euler Fermat theorem, polynomial congruence modulo P, Lagrange’s theorem, Application of Lagrange’s theorem, Chinese remainder theorem and its application, polynomial congruences with prime power moduli

 Unit-IV

 Quadratic residue and quadratic reciprocity law, Quadratic residues, Legendre’s symbol and its properties, evaluation of (−1/p) and (2/p), Gauss Lemma, the quadratic reciprocity law and its applications. 

Text Book:

 Introduction to analytic Number Theory by Tom M. Apostol. Chapters 1, 2, 5, 9. 

References: 

[1] Number Theory by Joseph H. Silverman.

 [2] Theory of Numbers by K.Ramchandra.

 [3] Elementary Number Theory by James K Strayer. 

[3] Elementary Number Theory by James Tattusall. 

MM 105                                                                                                                             Semester - I                                                             Paper - V: Discrete Mathematics 

Unit-I

 Mathematical Logic: Propositional logic, Propositional equivalences, Predicates and Quantifiers, Rule of inference, direct proofs, proof by contraposition, proof by contradiction. Boolean Algebra: Boolean functions and its representation, logic gates, minimizations of circuits by using Boolean identities and K - map. 

Unit-II

 Basic Structures: Sets representations, Set operations, Functions, Sequences and Summations. Division algorithm, Modular arithmetic, Solving congruences, applications of congruences. Recursion: Proofs by mathematical induction, recursive definitions, structural induction,generalized induction, recursive algorithms. 

Unit-III

 Counting: Basic counting principle, inclusion - exclusion for two - sets, pigeonhole principle, permutations and combinations, Binomial coefficient and identities, generalized permutations and combinations. Recurrence Relations: introduction, solving linear recurrence relations, generating functions, principle of inclusion - exclusion, applications of inclusion - exclusion. Relations: relations and their properties, representing relations, closures of relations, equivalence relations, partial orderings.

 Unit-IV

 Graphs: Graphs definitions, graph terminology, types of graphs, representing graphs, graph isomorphism, connectivity of graphs, Euler and Hamilton paths and circuits, Dijkstras algorithm to find shortest path, planar graphs Eulers formula and its applications, graph coloring and its applications. Trees: Trees definitions properties of trees, applications of trees BST, Haffman Coding, tree traversals: pre - order, in - order, post - order, prefix, infix, postfix notations, spanning tress DFS, BFS, Prims, Kruskals algorithms.

 Text Book:

 Discrete Mathematics and its Applicationsby Kenneth H. Rosen,

 References:

 [1] Discrete and Combinatorial Mathematicsby Ralph P. Grimaldi 

[2] Discrete Mathematics for Computer Scientists by Stein, Drysdale, Bogart 

[3] Discrete Mathematical Structures with Applications to Computer Scienceby J.P. Tremblay, R. Manohar 

[4] Discrete Mathematics for Computer Scientists and Mathematicians by Joe L. Mott, Abraham Kandel, Theoder P. Baker

SEMESTER _II

MM 201                                                                                                                           Semester - II                                                         Paper - I: Galois Theory

 Unit-I 

 Algebraic extensions of fields: Irreducible polynomials and Eisenstein criterion - Adjunction of roots - Algebraic extensions - Algebraically closed fields (Pages 281 to 299). 

Unit-II

 Normal and separable extensions: Splitting fields - Normal extensions - Multiple roots - Finite fields - Separable extensions (Pages 300 to 321). 

Unit-III

 Galois theory: Automorphism groups and fixed fields - Fundamental theorem of Galois theory - Fundamental theorem of Algebra (Pages 322 to 339). 

Unit-IV

 Applications of Galois theory to classical problems: Roots of unity and cyclotomic polynomials - Cyclic extensions - Polynomials solvable by radicals - Ruler and Compass constructions. (Pages 340 - 364). 

Text Book: 

Basic Abstract Algebra by S.K. Jain, P.B. Bhattacharya, S.R. Nagpaul. 

References: 

[1] Topics in Algebra by I.N. Herstein.

 [2] Elements of Modern Algebra by Gibert& Gilbert. 

[3] Abstract Algebra by Jeffrey Bergen.

 [4] Basic Abstract Algebra by Robert B Ash.

 MM 202                                                                                                                           Semester - II                                              Paper - II: Lebesgue Measure & Integration 

Unit-I

 Algebra of sets - Borel sets - Outer measure - Measurable sets and Lebesgue measure - A non - measurable set - Measurable functions - Littlewood three principles.

 Unit-II 

The Riemann integral - The Lebesgue integral of a bounded function over a set of finite measure - The integral of a non - negative function - The general Lebesgue integral. 

Unit-III 

Convergence in measure - Differentiation of a monotone functions - Functions of bounded variation. Unit-IV

 Differentiation of an integral - Absolute continuity - The Lp - spaces - The Minkowski and Holders inequalities - Convergence and completeness. 

Text Book: 

Real Analysis (3rd Edition)(Chapters 3, 4, 5 ) by H. L. Royden Pearson Education (Low Price Edition).

 References:

 [1] Lebesgue measure and Integration by G.de Barra. 

[2] Measure and Integral by Richard L.Wheeden, Anotoni Zygmund. 

 MM 203                                                                                                                           Semester - II                                                        Paper - III: Complex Analysis

 Unit-I

 Regions in the Complex Plane - Functions of a Complex Variable - Mappings - Mappings by the Exponential Function - Limits - Limits Involving the Point at Infinity - Continuity - Derivatives - Cauchy Riemann Equations - Sufficient Conditions for Differentiability - Analytic Functions - Harmonic Functions - Uniquely Determined Analytic Functions - Reflection Principle - The Exponential Function - The Logarithmic Function - Some Identities Involving Logarithms - Complex Exponents - Trigonometric Functions - Hyperbolic Functions 

Unit-II

 Derivatives of Functions w(t) - Definite Integrals of Functions w(t) - Contours - Contour Integrals - Some Examples - Examples with Branch Cuts - Upper Bounds for Moduli of Contour Integrals Anti derivatives - Cauchy Goursat Theorem - Simply Connected Domains - Multiply Connected Domains - Cauchy Integral Formula - An Extension of the Cauchy Integral Formula - Liouville’s Theorem and the Fundamental Theorem of Algebra - Maximum Modulus Principle. 

Unit-III 

Convergence of Sequences - Convergence of Series - Taylor Series - Laurent Series - Absolute and Uniform Convergence of Power Series - Continuity of Sums of Power Series - Integration and Differentiation of Power Series - Uniqueness of Series Representations - Isolated Singular Points - Residues - Cauchy’s Residue Theorem - Residue at Infinity - The Three Types of Isolated Singular Points - Residues at Poles - Examples - Zeros of Analytic Functions - Zeros and Poles - Behavior of Functions Near Isolated Singular Points.

 Unit-IV

 Evaluation of Improper Integrals - Improper Integrals from Fourier Analysis - Jordan’s Lemma - Indented Paths - Definite Integrals Involving Sines and Cosines - Argument Principle - Rouche’s Theorem - Linear Transformations - The Transformation w = 1/z - Mappings by 1/z - Linear Fractional Transformations - An Implicit Form - Mappings of the Upper Half Plane.

 Text Book:

 Complex Variables with applications by James Ward Brown, Ruel V Churchill.

 References:

 [1] Complex Analysis by Dennis G.Zill.

 [2] Complex Variables by Stevan G. Krantz.

 [3] Complex Variables with Applications by S.Ponnusamy, Herb Silverman.

 [4] Complex Analysis by Joseph Bak, Donald J. Newman. 

 MM 204                                                                                                                           Semester - II                                                                          Paper - IV: Topology

 Unit-I

 Topological Spaces: The Definition and examples - Elementary concepts - Open bases and open subbases - Weak topologies.

 Unit-II

 Compactness: Compact spaces - Products of spaces - Tychonoff’s theorem and locally compact spaces - Compactness for metric spaces - Ascoli’s theorem. 

Unit-III

 Separation: T1 - spaces and Hausdorff spaces - Completely regular spaces and normal spaces - Urysohn’s lemma and the Tietze extension theorem - The Urysohn imbedding theorem. 

Unit-IV

 Connectedness: Connected spaces - The components of a spaces - Totally disconnected spaces - Locally connected spaces. 

Text Book:

 Introduction to Topology and Modern Analysis (Chapters 3,4,5,6) By G.F. Simmon’s Tata Mc Graw Hill Edition.

 References:

 [1] Introductory Topology by Mohammed H. Mortad. 

[2] Explorations in Topology by David Gay.

 [3] Encyclopedia of General Topology by Hart, Nagata, Vanghan.

 [4] Elementary Topology by Michael C. Gemignani. 

 MM 205                                                                                                                      Semester - II                                        Paper - V: Theory of Ordinary Differential Equations 

Unit-I

 Linear differential equations of higher order: Introduction - Higher order equations - A Modelling problem Linear Independence - Equations with constant coefficients Equations with variable coefficients - Wronskian - Variation of parameters - Some Standard methods.

 Unit-II

 Existence and uniqueness of solutions: Introduction - Preliminaries - Successive approximations - Picards theorem - Continuation and dependence on intial conditions - existence of solutions in the large - existence and uniqueness of solutions of systems - fixed point method.

 Unit-III

 Analysis and methods of non - linear differential equations: Introduction - Existence theorem Extremal solutions - Upper and Lower solutions - Monotone iterative method and method of quasi linearization - Bihari’s inequality, Application of Bihari’s inequality

 Unit-IV 

Oscillation theory for linear Differential Equation of Second order: The adjoint equation - Self adjoint linear differential equation of second order - Abel’s formula - the number of zeros in a finite interval - The sturm separation theorem - the strum comparison theorem the sturmpicone the Bocher Osgood theorem - A special pair of solution - Oscillation on half axis. 

Text Book: 

An Introduction to Ordinary Differential Equations by Earl A Coddington. 

References:

 [2] Differential Equations by Edward, Penny, Calvis.

 [3] Differential Equation by Harry Hochstardt. 

PG II Year Syllabus 2018-19(III SEM)

DEPARTMENT OF MATHEMATICS 

OSMANIA UNIVERSITY 

M.Sc. Mathematics

 MM301                                                                                                                     Semester III

      Paper-I Complex Analysis 

 UNIT-I
 Regions in the Complex Plane -Functions of a Complex Variable - Mappings -Mappings by the Exponential Function- Limits - Limits Involving the Point at Infinity - Continuity -Derivatives - Cauchy–Riemann Equations -Sufficient Conditions for Differentiability - Analytic Functions - Harmonic Functions -Uniquely Determined Analytic Functions - Reflection Principle - The Exponential Function -The Logarithmic Function -Some Identities Involving Logarithms -Complex Exponents -Trigonometric Functions -Hyperbolic Functions

 UNIT-II 
Derivatives of Functions w(t) -Definite Integrals of Functions w(t) - Contours -Contour Integrals - Some Examples -Examples with Branch Cuts -Upper Bounds for Moduli of Contour Integrals –Anti derivatives -Cauchy–Goursat Theorem -Simply Connected Domains- Multiply Connected DomainsCauchy Integral Formula -An Extension of the Cauchy Integral Formula -Liouville’s Theorem and the Fundamental Theorem of Algebra -Maximum Modulus Principle

 UNIT-III
 Convergence of Sequences - Convergence of Series - Taylor Series -Laurent Series -Absolute and Uniform Convergence of Power Series- Continuity of Sums of Power Series - Integration and Differentiation of Power Series - Uniqueness of Series Representations-Isolated Singular Points - Residues -Cauchy’s Residue Theorem - Residue at Infinity - The Three Types of Isolated Singular Points - Residues at Poles -Examples -Zeros of Analytic Functions -Zeros and Poles -Behavior of Functions Near Isolated Singular Points

 UNIT-IV
Evaluation of Improper Integrals -Improper Integrals from Fourier Analysis - Jordan’s Lemma - Indented Paths - - Definite Integrals Involving Sines and Cosines - Argument Principle -Rouche ́’s Theorem -Linear Transformations -The Transformation w = 1/z - Mappings by 1/z -Linear Fractional Transformations -An Implicit Form -Mappings of the Upper Half Plane

Text: James Ward Brown, Ruel V Churchill, Complex Variables with applications.

MM302                                                                                                                 Semester-III  
 Paper-II Functional Analysis

 Unit –I
 NORMED LINEAR SPACES: Definitions and Elementary Properties, Subspace, Closed Subspace, Finite Dimensional Normed LinearSpaces and Subspaces, Quotient Spaces, Completion of Normed Spaces.

 Unit-II 
HILBERT SPACES: Inner Product Space, Hilbert Space, Cauchy-Bunyakovsky-Schwartz Inequality, Parallelogram Law, Orthogonality, Orthogonal Projection Theorem, Orthogonal Complements, Direct Sum, Complete Orthonormal System, Isomorphism between Separable HilbertSpaces.

 Unit-III 
LINEAR OPERATORS: Linear Operators in Normed Linear Spaces, Linear Functionals, The Space of Bounded Linear Operators, Uniform Boundedness Principle,Hahn-Banach Theorem, Hahn-Banach Theorem for Complex Vector and Normed Linear Space, The General Form of Linear Functionals in Hilbert Spaces.

Unit-IV
 FUNDAMENTAL THEOREMS FOR BANACH SPACES AND ADJOINT OPERATORS IN HILBERT SPACES: Closed Graph Theorem, Open Mapping Theorem, Bounded Inverse Theorem, Adjoint Operators, Self-Adjoint Operators, Quadratic Form, Unitary Operators, Projection Operators.

Text Book: A First Course in Functional Analysis-Rabindranath Sen, Anthem Press An imprint of Wimbledon Publishing Company.

 Reference: 1. Introductory Functional Analysis- E.Kreyzig- John Wilely and sons, New York, 2. Functional Analysis, by B.V. Limaye 2nd Edition. 3. Introduction to Topology and Modern Analysis- G.F.Simmons. Mc.Graw-Hill International Edition.

MM –303 A                                                                                                           Semester -III 
 Paper-III (A) Discrete Mathematics 

UNIT- I 
LATTICES: Partial Ordering – Lattices as Posets – some properties of Lattices – Lattices as Algebraic Systems – Sublattices, Direct products and Homomorphisms – some special Lattices – Complete, complemented and distributive lattices. (Pages 183-192, 378-397 of [1])

UNIT- II
BOOLEAN ALGEBRA: Boolean Algebras as Lattices – Boolean Identities – the switching Algebra – sub algebra, Direct product and homomorphism – Join irreducible elements – Atoms (minterms) – Boolean forms and their equivalence – minterm Boolean forms – Sum of products canonical forms – values of Boolean expressions and Boolean functions – Minimization of Boolean functions – the Karnaugh map method. (Pages 397 – 436 of [1])

 UNIT- III
 GRAPHS AND PLANAR GRAPHS : Directed and undirected graphs – Isomorphism of graphs – subgraph – complete graph – multigraphs and weighted graphs – paths – simple and elementary paths – circuits – connectedness – shortest paths in weighted graphs – Eulerian paths and circuits – Incoming degree and outgoing degree of a vertex - Hamiltonian paths and circuits – Planar graphs – Euler’s formula for planar graphs. (Pages 137-159, 168-186 of [2])

UNIT- IV 
TREES AND CUT-SETS: Properties of trees – Equivalent definitions of trees - Rooted trees – Binary trees – path lengths in rooted trees – Prefix codes – Binary search trees – Spanning trees and Cut-sets – Minimum spanning trees (Pages 187-213 of [2])

Text Books:- [1] J P Tremblay and R. Manohar: Discrete Mathematical Structures with applications to Computer Science, McGraw Hill Book Company [2] C L Liu : Elements of Discrete Mathematics, Tata McGraw Hill Publishing Company Ltd. New Delhi. (Second Edition).

MM – 304A                                                                                                                  Semester III  Paper IV A   Operations Research       

 Unit I 

Formulation of Linear Programming problems, Graphical solution of Linear Programming problem, General formulation of Linear Programming problems, Standard and Matrix forms of Linear Programming problems, Simplex Method, Two-phase method, Big-M method, Method to resolve degeneracy in Linear Programming problem, Alternative optimal solutions. Solution of simultaneous equations by simplex Method, Inverse of a Matrix by simplex Method, Concept of Duality in Linear Programming, Comparison of solutions of the Dual and its primal.

 Unit II
 Mathematical formulation of Assignment problem, Reduction theorem, Hungarian Assignment Method, Travelling salesman problem, Formulation of Travelling Salesman problem as an Assignment problem, Solution procedure. Mathematical formulation of Transportation problem, Tabular representation, Methods to find initial basic feasible solution, North West corner rule, Lowest cost entry method, Vogel's approximation methods, Optimality test, Method of finding optimal solution, Degeneracy in transportation problem, Method to resolve degeneracy, Unbalanced transportation problem.

Unit III 
Concept of Dynamic programming, Bellman's principle of optimality, characteristics of Dynamic programming problem, Backward and Forward recursive approach, Minimum path problem, Single Additive constraint and Multiplicatively separable return, Single Additive constraint and Additively separable return, Single Multiplicatively constraint and Additively separable return.

Unit-IV
 Historical development of CPM/PERT Techniques - Basic steps - Network diagram representation - Rules for drawing networks - Forward pass and Backward pass computations - Determination of floats - Determination of critical path - Project evaluation and review techniques updating.

 Text Books: [1] S. D. Sharma, Operations Research.
 [2] Kanti Swarup, P. K. Gupta and Manmohan, Operations Research.
 [3] H. A. Taha, Operations Research – An Introduction. 

PG TimeTables 2019-20

ST.PIOUS X DEGREE & PG COLLEGE FOR WOMEN

DEPARTMENT OF MATHEMATICS

M.Sc TIMETABLE FOR SEMESTER I & III (2019-20)

II PG

DAY	1	2		3	4	5		6
Monday	P-II (Kalyani)	P-V (Sparsha)		P-III (Sridevi)	Library		P-I (Mehrunissa)	P-IV  (Sridevi)
Tuesday	P-I (Mehrunissa)	P-III (Sridevi)		P-V (Sparsha)	P-IV  (Sridevi)	P-II (Kalyani)		Sports
Wednesday	P-V (Sparsha)	P-I (Mehrunissa)		P-II (Kalyani)	P-IV  (Sridevi)			Seminar (Sparsha)
Thursday	P-I (Mehrunissa)			P-V (Sparsha)	P-IV  (Sridevi)	P-II (Kalyani)		Seminar (Mehrunissa)
Friday	P-III (Sridevi)			P-II (Kalyani)	P-IV  (Sridevi)	P-V (Sparsha)		P-I (Mehrunissa)
Saturday	P-III (Sridevi)	P-V (Sparsha)	P-II (Kalyani)		P-III (Sridevi)

I PG

DAY	1	2		3	4	5		6
Monday	P-II    (Jyothi)	Library		P-III (Kalyani)	P-IV (Kalyani)		P-II    (Jyothi)	Seminar (Mehrunissa)
Tuesday	P-II    (Jyothi)	P-III (Kalyani)	P-I (Mamatha)			P-V (Sridevi)		P-IV (Kalyani)
Wednesday	P-III (Kalyani)	P-V (Sridevi)		P-III (Kalyani)	Sports		P-II    (Jyothi)	P-IV (Kalyani)
Thursday	P-V (Sridevi)		P-IV (Kalyani)		P-I (Mamatha)		P-II    (Jyothi)
Friday	P-III (Kalyani)	Seminar (Sparsha)	P-I (Mamatha)			P-IV (Kalyani)		P-V (Sridevi)
Saturday	P-III (Kalyani)	P-I (Mamatha)	P-V (Sridevi)		P-IV (Kalyani)	-